Concept explainers
a.
Prove that a constant d can be added or subtracted to each
a.
Explanation of Solution
Calculation:
The model used to predict
To this model a constant d is added,
The mean response due to the
Where,
The mean response due to the
Where,
The overall mean response of Y is given below:
Where,
The total sum of squares is given below:
The error sum of squares is given below:
Using the similar method, the sum of squares due to factor A and B are calculated.
Sum of squares due to factor A:
Sum of squares due to factor B:
From all the sum of squares it can observed that the addition of a constant d has no effect on the sum of squares.
b.
Identify the change in the sum of squares due to multiplication of constant c.
Identify the changes in the F-statistic for factor A and B.
Find the effect of
b.
Answer to Problem 13E
The sum of squares remains unchanged and the F-statistic for factor A and B also remains unchanged.
The conclusions for ANOVA remains unchanged by using
Explanation of Solution
Calculation:
The model used to predict
To this model a constant c is multiplied,
Then the sum of squares would have the square of the constant c and it is shown below:
Total sum of squares:
Sum of squares due to factor A:
Sum of squares due to factor B:
Sum of squares due to error:
Mean sum of squares for factor A:
Mean sum of squares for factor B:
Mean sum of squares for error:
Thus, the F-statistic for factor A would be,
For factor B:
From part (a) the addition of constant d has no effect on ANOVA and also the multiplication of constant c has no effect on ANOVA.
Hence, coding the model as
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Chapter 11 Solutions
Probability and Statistics for Engineering and the Sciences
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL